study 4

A 99% Confidence interval estimate can be interpreted to mean that

If all possible samples are taken and confidence intervals estimates are developed, 99% of them would include the true population mean somewhere within their interval. & you have 99% confidence that you have selected a sample whose interval does include the population

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if:

a two tail test for mu is used

If an event A and event B cannot occur at the same time, the events A and B are said to be

mutually exclusive

In the construction of confidence intervals, if all other quantities are unchanged, as increase in the sample size will lead to a _____ interval

narrower

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% Confidence interval (0.438. 0.642) Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within + 0.08 using 95% confidence?

150

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75

198

A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false.

False

A confidence interval provides a value that, with a certain measure of confidence is the population parameter of interest

False

For a given sample size n and a population standard deviation sigma, the width of the confidence interval for the population mean is wider, the smaller the confidence level 100(1-alpha)%

False

Like z distribution, the tdf distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it

False

Which of the following represents an appropriate set of hypotheses?

H0: u=0 ; HA: u ≠to 0

Given a sample mean of 12.5 - drawn from a normal population, a sample of size 25 and a sample variance of 2.4 - find a 99% confidence interval for the population mean

(11.633,13.367)

Professors of accountancy are in high demand at American Universities. A random sample of 28 accounting professors found the average salary was 135 thousand with a standard deviation of 16 thousand. Assume the distribution is normally distributed. Construct a 90% confidence interval for the salary of new accounting professors. Answers are in thousands of dollars.

(129.8506,140.1494)

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice. The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35. Construct a 99% Confidence interval for the average number of free throws in practice.

(210.6,239.4)

A company decided to test the hypothesis that the average time a company's employees are spending to check their private emails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The alpha is set to 0.05. The p-value for this hypothesis test would be _______.

0.0128

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?

A larger sample size reduces the margin of error

A 99% confidence interval for the population mean yields the following results [3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with H0:mu =0, Ha:mu≠0 ?

Do not reject H0; we cannot conclude that the mean differs from zero.

Which of the following is the correct formula for the margin of error in the interval estimation of p?

E = Za/2 * sqr[(p(1-p))/(n)]

Which of the following is not true about the student's t distribution?

It is used to construct confidence intervals for the population mean when the population standard deviation is known

A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642) Based on the interval above is the population proportion of females equal to 0.60?

Maybe. 0.60 is believable value of the population proportion based on the information above

In general, the null and alternative hypothesis are ____________.

Mutually Exclusive

To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42. If we choose a 5% significance level, we. _________.

Reject the null hypothesis and conclude that the mean IQ is greater than 100

Which of the following types of tests may be performed?

Right hand test, left hand test and two sided test

When the required sample size calculated by using a formula is not a whole number, what is the best choice for the required sample size?

Round the result of the calculation up to the nearest whole number

A ________ is a numerical quantity not computed from the data of a sample and is the size of the critical region used in reaching a decision on whether or not to reject the null hypothesis.

Test Statistic

If the type I error (alpha) for a given test is to be decreased, then for a fixed sample size n

The Type II error will increase

A Type I error is committed when we reject the null hypothesis, which is actually true.

True

If, as a result of a hypothesis test, we do not reject the null hypothesis when it is false, then we have committed?

Type II Error

A type II error is committed when:

We fail to reject a null hypothesis that is false

A 90% confidence interval is constructed for the population mean. If a 95% confidence interval ad been constructed instead, the width of the interval would have been_____ and the probability of making an error would have been __________

Wider & Smaller

A 95% Confidence interval estimate can be interpreted to mean that

You have 95% confidence that you have selected a sample whose interval does include the population mean.

Vermont based green mountain coffee roasters dominates the market for single serve coffee in the United states, with its subsidiary Keurig accounting for approximately 70% of the sales. But Keurig's patent on k-cups is expected to expire this year, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blen and finds that 47% of its customers strongly prefer its French roast to that green mountain coffee roasters. After tweaking its recipe the competitor conducts test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of the consumers to green mountain coffee roasters French roast. What is the value of the appropriate test statistics to test this claim?

Z = 0.721

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when sigma is known?

if the population standard deviation is greater, the interval is wider

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this person is selling at lower markups. He knows that the long-run average markup in his lot is 5,600. He takes a random sample of 16 of the new salespersons sales and finds an average markup of 5000 and a standard deviation of 800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?

t15 = -3.00